Quadric Surfaces

The equation is represented by which graph?

x² - y² + z² = 1

• I

• II

• III

• IV

The equation is represented by which graph?

x² + 4y² + 9z² = 1

• V

• VI

• VII

• VIII

The equation is represented by which graph?

y² = x² + 2z²

• I

• II

• III

• IV

The equation is represented by which graph?

9x² + 4y² + z² = 1

• I

• II

• III

• IV

The equation is represented by which graph?

-x² + y² - z² = 1

• I

• II

• III

• IV

The equation is represented by which graph?

y = x² - z²

• V

• VI

• VII

• VIII

For the quadric surface given, identify the center:

9x² + 4y² + 36z² - 18x + 144z + 152 = 0

• (-1, 0, -2)

• (-1, 0, 2)

• (1, 0, -2)

• (1, 0, 2)

For the quadric surface given, identify the traces:

9x² + 4y² + 36z² - 18x + 144z + 152 = 0

• ellipses

• ellipses & circles

• ellipses & parabolas

• ellipses & hyperbolas

For the quadric surface given, identify the vertex:

4y² + z² - x - 16y - 4z + 20 = 0

• (0, -2, -2)

• (0, -2, 2)

• (0, 2, -2)

• (0, 2, 2)

The following equation represents:

y + 3 = (z - 1)²

• a cylinder

• an elliptical cylinder

• a hyperbolic cylinder

• a parabolic cylinder